Neural Differentiable Integral Control Barrier Functions for Unknown Nonlinear Systems with Input Constraints

In this paper, we propose a deep learning based control synthesis framework for fast and online computation of controllers that guarantees the safety of general nonlinear control systems with unknown dynamics in the presence of input constraints. Towards this goal, we propose a framework for simultaneously learning the unknown system dynamics, which can change with time due to external disturbances, and an integral control law for trajectory tracking based on imitation learning. Simultaneously, we learn corresponding safety certificates, which we refer to as Neural Integral Control Barrier Functions (Neural ICBF's), that automatically encode both the state and input constraints into a single scalar-valued function and enable the design of controllers that can guarantee that the state of the unknown system will never leave a safe subset of the state space. Finally, we provide numerical simulations that validate our proposed approach and compare it with classical as well as recent learning based methods from the relevant literature.